tr.v. ad·dict·ed, ad·dict·ing, ad·dicts
1. To cause to become physiologically or psychologically dependent on a habit-forming substance: The thief was addicted to cocaine.
2. To occupy (oneself) with or involve (oneself) in something habitually or compulsively: The child was addicted to video games.
1. One who is addicted, as to narcotics or a compulsive activity.
2. A devoted adherent; a fan: “We are all... addicts of change” (Christopher Lasch).
See number 2 of both noun and verb. It makes sense now, doesn't it. Words can have more than one meaning.